Problem: How many terms of the arithmetic sequence 88, 85, 82, $\dots$ appear before the number $-17$ appears?
Answer: The common difference $d$ is $85-88 = -3$, so the $n^{\text{th}}$ term in the arithmetic sequence is $88 - 3(n - 1) = 91 - 3n$.  If $91 - 3n = -17$, then $3n = (91 + 17) = 108$, so $n = 108/3 = 36$.  Hence, $-17$ is the $36^{\text{th}}$ term in this arithmetic sequence, which means that $36 - 1 = \boxed{35}$ terms appear before $-17$ does.